3. Fed-Batch Fermentations
 

3.1. Fixed volume fed-batch
3.2. Variable volume fed-batch
3.3. Advantages and disadvantages of fed-batch culture
3.4. Equipment
3.4.1. Vessels
3.4.2. Pumps
3.5. Control techniques for fed-batch fermentations
3.6. Modelling of fed-batch reactors
3.6.1. Fixed volume fed-batch
3.6.2. Variable volume fed-batch
3.6.3. Models of possible situations that may occur in fed-batch fermentation
3.7. Parameters used to control fed-batch fermentations
3.7.1. Calorimetry
3.7.2. Specific growth rate
3.7.3. Substrate (carbon or nitrogen source)
3.7.4. By-product concentration
3.7.5. Inductive, enhancer or enrichment components
3.7.6. Respiratory quotient
3.7.7. General feeding mode
3.7.8. Proton production rate
3.7.9. Fluorescence
3.8. Parameters to start and finish the feed, and stop the fed-batch fermentation
3.9. Preliminary knowledge required to implement fed-batch
3.10. Algorithms for operating a fed-batch reactor at optimum specific growth rate (model independent and applicable to adapting systems)


3.11. Some examples of fed-batch use in industry



 

Two basic approaches to the fed-batch fermentation can be used: the constant volume fed-batch culture - Fixed Volume Fed-Batch - and the Variable Volume Fed-Batch. The kinetics of the two types of fed-batch culture will be described in section 3.6.


3.1. Fixed volume fed-batch

In this type of fed-batch, the limiting substrate is fed without diluting the culture.

The culture volume can also be maintained practically constant by feeding the growth limiting substrate in undiluted form, for example, as a very concentrated liquid or gas (ex. oxygen).

Alternatively, the substrate can be added by dialysis or, in a photosynthetic culture, radiation can be the growth limiting factor without affecting the culture volume5.

A certain type of extended fed-batch - the cyclic fed-batch culture for fixed volume systems - refers to a periodic withdrawal of a portion of the culture and use of the residual culture as the starting point for a further fed-batch process. Basically, once the fermentation reaches a certain stage, (for example, when aerobic conditions cannot be maintained anymore) the culture is removed and the biomass is diluted to the original volume with sterile water or medium containing the feed substrate22. The dilution decreases the biomass concentration and result in an increase in the specific growth rate (see mathematical description in section 3.6). Subsequently, as feeding continues, the growth rate will decline gradually as biomass increases and approaches the maximum sustainable in the vessel once more, at which point the culture may be diluted again26.

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3.2. Variable volume fed-batch

As the name implies, a variable volume fed-batch is one in which the volume changes with the fermentation time due to the substrate feed. The way this volume changes it is dependent on the requirements, limitations and objectives of the operator.

The feed can be provided according to one of the following options:

(i) the same medium used in the batch mode is added;

(ii) a solution of the limiting substrate at the same concentration as that in the initial medium is added; and

(iii) a very concentrated solution of the limiting substrate is added at a rate less than (i), (ii) and (iii) 21.

This type of fed-batch can still be further classified as repeated fed-batch process or cyclic fed-batch culture, and single fed-batch process.

The former means that once the fermentation reached a certain stage after which is not effective anymore, a quantity of culture is removed from the vessel and replaced by fresh nutrient medium. The decrease in volume results in a increase in the specific growth rate, followed by a gradual decrease as the quasi-steady state is established.

The latter type refers to a type of fed-batch in which supplementary growth medium is added during the fermentation, but no culture is removed until the end of the batch. This system presents a disadvantage over the fixed volume fed-batch and the repeated fed-batch process: much of the fermentor volume is not utilized until the end of the batch and consequently, the duration of the batch is limited by the fermentor volume26.

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3.3. Advantages and disadvantages of the fed-batch reactors

 

Fed-batch fermentation is a production technique in between batch and continuous fermentation12. A proper feed rate, with the right component constitution is required during the process8.

Fed-batch offers many advantages over batch and continuous cultures. From the concept of its implementation it can be easily concluded that under controllable conditions and with the required knowledge of the microorganism involved in the fermentation, the feed of the required components for growth and/or other substrates required for the production of the product can never be depleted and the nutritional environment can be maintained approximately constant during the course of the batch. The production of by-products that are generally related to the presence of high concentrations of substrate can also be avoided by limiting its quantity to the amounts that are required solely for the production of the biochemical. When high concentrations of substrate are present, the cells get "overloaded", this is, the oxidative capacity of the cells is exceeded, and due to the Crabtree effect, products other than the one of interest are produced, reducing the efficacy of the carbon flux. Moreover, these by-products prove to even "contaminate" the product of interest, such as ethanol production in baker's yeast production, and to impair the cell growth reducing the fermentation time and its related productivity.

Sometimes, controlling the substrate is also important due to catabolic repression. Since this method usually permits the extension of the operating time, high cell concentrations can be achieved and thereby, improved productivity [mass of product/(volume.time)]. This aspect is greatly favored in the production of growth-associated products1.

Additionally, this method allows the replacement of water loss by evaporation and decrease of the viscosity of the broth such as in the production of dextran and xanthan gum13, by addition of a water-based feed.

As previously mentioned, fed-batch might be the only option for fermentations dealing with toxic or low solubility substrates.

When dealing with recombinant strains, fed-batch mode can guarantee the presence of an antibiotic throughout the course of the fermentation, with the intent of keeping the presence of an antibiotic-marked plasmid. Since the growth can be regulated by the feed, and knowing that in many cases a high growth rate can decrease the expression of encoded products in recombinant products, the possibility of having different feeds and feed modes makes fed-batch an extremely flexible tool for control in these cases7, 8.

Because the feed can also be multisubstrate, the fermentation environment can still be provided with required protease inhibitors that might degrade the product of interest, metabolites and precursors that increase the productivity of the fermentation19.

Finally, in a fed-batch fermentation, no special piece of equipment is required in addition to that one required by a batch fermentation, even considering the operating procedures for sterilization and the preventing of contamination12.

A cyclic fed-batch culture has an additional advantage: the productive phase of a process may be extended under controlled conditions. The controlled periodic shifts in growth rate provide an opportunity to optimize product synthesis, particularly if the product of interest is a secondary metabolite whose maximum production takes place during the deceleration in growth22.

 

As a summary of what was described above, fed-batch mode of fermentation has the following features:

       Disadvantages:

 
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3.4. Equipment

No special piece of equipment is required over the equipment required for batch13. However, some considerations should be made over the equipment used for a fed-batch fermentation.

3.4.1. Vessels

The vessels, particularly those used for the acid and base control, must be constructed from a non-toxic, corrosion-resistant material which is capable of withstanding repeated sterilization cycles13. Figure 3.4.1. Illustrates two methods of assembling vessels for easy transfer of either inoculum or medium to the fermentor.

 

Figure 3.4.1. Holding vessels. A. Screw-neck borosilicate glass vessel with medium/inoculum addition assembly. (a) Stainless steel rod; (b) Silicon tubing; (c) Silicon disc; (d) Hypodermic needle; (e) Air vent; (f) Screw cap; (g) Magnetic bar. B. Aspirator-type vessel for introducing an inoculum of filamentous fungi into the fermentor. (a) Cotton-wool plug; (b) Magnetic stirrer bar13.

 

 

3.4.2. Pumps

There are two types of pumps which are suitable for the aseptic pumping of small volumes of culture media: the peristaltic pump and the diaphragm-dosing pump. Other pumps are unsuitable because they are difficult to sterilize and cannot be used for pumping small volumes13.

The peristaltic pump is typically constituted by a main body that comprises both the drive motor and electrics, and the rotating unit of rollers. This unit of rollers occludes the tube which, as it recovers to its original size passes to the nest roller until is expelled, as the unit moves round. The flow rate can be varied by either the speed setting or by changing the diameter of the tube being used.

The diaphragm-dosing pump consists of a main body and a detachable heat-sterilizable head. The fluid is sucked in to the pump head. The suction inlet tube then closes and the pressure discharge tube opens and forces the fluid out. The suction and pressure forces in the pump head are generated by the reciprocating action of both the diaphragm plunger and the return spring. For a more accurate description of these pumps, reference 13 can be consulted.
 

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3.5. Control techniques for fed-batch fermentation

Adaptive control is the name given to a control system in which the controller learns about the process by acquiring data from a certain process and keeps on updating a control model. A parameter estimator monitors the process and estimates the process dynamics in terms of the parameters of a previously defined mathematical model of the process. A control design algorithm is then used to generate controller coefficients from those estimates, and a controller sets up the required control signals to the devices controlling the process. An extremely important feature of an adaptive controller is the structure of the model used by the parameter estimator to analyze estimates of process dynamics. The process can be described by a set of mass balance equations, whose quantities can be measured directly or indirectly26 . Figure 3.5.1. describes schematically the concept.

 

Figure 3.5.1. Adaptive control: the controller compares the estimates from a mathematical model applied to the system to the readings obtained from the fermentation process. The controller then sends the signal to the device controlling the fermentation, for example, by increasing or decreasing a flow rate.

The optimal strategy for the fed-batch fermentation of most organisms is to feed the growth-limiting substrate at the same rate that the organism utilizes the substrate, this is, to match the feed rate with demand for the substrate.

Four basic approaches have been used in attempts to balance substrate feed with demand (listed in order of increasing accuracy and/or complexity):

(i) open-loop control schemes in which feed is added according to historical data or predicted data;

(ii) indirect control of substrate feed based on non-feed source parameters such as pH, offgas analysis, dissolved O2 or concentrations of organic products;

(iii) indirect control schemes based on mass balance equations, the values of which are calculated from data obtained by sensors; and

(iv) direct control schemes based on direct, on-line measurements substrates9.

Better and more flexible control may be obtained when there is direct measurement of substrate or an excreted metabolite in the medium, which can be used to influence feeding rates to the fermentation. This can be done off-line or semi-on-line, but on-line measurements are more useful because of

Regardless the type of control, the design is strongly influenced by both mathematical model availabilities and measurement possibilities14.

Control and optimization of bioreactors is strongly influenced by the quality of the sensors available for crucial response variables4. Of primary importance is the ratio of the dynamic parameters of the sensor to those of the process. When these variables cannot be measured easily or quickly enough, a mathematical model must be used in some way in place of feedback information.

When an exact mathematical model is at disposal, an open-loop process control can be proposed which generally proves to be insufficient14. The advantage of a feedback control is that a response to unforeseen and unexpected conditions during the fermentation is achieved and the process is controlled within the desired limits 29.

An indirect feedback control utilizes an observable parameter, such as dissolved oxygen, pH, respiratory quotient, partial pressure of CO2, culture fluorescence or by-product formation, which is closely related to the course of microbial fermentation. As examples of fed-batch systems using this concept, one can mention the pH-stat - a system in which the feed is provided depending on the pH, - and the DO-stat - a system in which the feed is provided depending on the reading of the dissolved oxygen24, 29.

A direct feedback controller uses the concentration of limiting substrate in the culture medium as a feedback feed -related parameter for control. A direct feedback control can have the disadvantage of not being very feasible due to the difficulty associated with obtaining accurate on-line measurements of substrate concentrations or even by the absence of on-line sensors for the important compound to control14. The advantage of a feedback control is that a response to unforeseen and unexpected conditions during the fermentation is achieved and the process is controlled within the desired limits 29.

 

A feedback control can be implemented accordingly to not only a single measurement, but also to obtain a finer control action in a dual-level system. Turner at al. 25, describes a control method applied to a fed-batch culture of recombinant Escherichia coli in which a two-level control was preferred because it provided much greater flexibility and better control over the substrate concentration in the medium and the production of by-products 25, 29.

 

As compared with the batch fermentation, two more parameters need to be specified to determine the operating conditions of a fed-batch fermentation: feed and initial feeding time. These parameters are usually process and/or microorganism specific and the parameters commonly used to define them are explained in section 3.7.

 

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3.6. Modeling fed-batch fermentations

 

3.6.1. Fixed volume fed-batch

The mathematical development that is going to be presented here has the following assumptions22:

The equations that describe the system in terms of specific growth rate, biomass and product concentration (for both growth and non-growth associated products) with time are the following:

    Parameter
    Equation
Equation #
Specific Growth Rate u = (F . Yx/s) / x

    (3.6.1.1)

Biomass (as a function of time) xt = xo + F . Y x/s . t

    (3.6.1.2)

Product Concentration
(non-growth associated)
P= Pi + qp . xo . t + qp . F . Y x/s . t2 /2

    (3.6.1.3)

Product Concentration
(non-growth associated)
P= Pi + rp . t

    (3.6.1.4)


  • x is the biomass [mass biomass/volume]
  • xo is the biomass in the beginning of the fermentation [mass biomass/volume]
  • t is time
  • F is the substrate feed rate [mass substrate/(volume.time)] and
  • Y x/s is the yield factor [mass biomass/mass substrate]
  • u is the specific growth rate [time-1]
  • P is the product concentration {mass product/volume] and
  • qp is the specific production rate of product [mass product/(mass biomass . time)
  • rpis the product formation rate [mass product/(volume . time)]
  • From equations (3.6.1.1) and (3.6.1.2), it can be observed that

    (i) the specific growth rate decreases with time because the biomass (in the denominator) is increasing with time and

    (ii) the biomass increases linearly with time.

    The product variation with time will depend on its being growth or non-growth associated, this is, will depend on qp (specific product formation defined as the product formation rate divided by the biomass) being dependent on the specific growth rate or not, respectively.

    To obtain the derivations that yielded these equations, please click here.

    Figure 3.6.1.1. depicts the typical behavior of a fixed-volume fed-batch culture.

     

     

    Figure 3.6.1.1. Time profiles for a fixed-volume fed-batch culture. u= specific growth rate, x = biomass concentration, S(GLS) = growth limiting substrate, SN = any other substrate other than the S(GLS), P(nga) is the non-growth associated product and P(ga) is the growth associated profile for product concentration.

     

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    3.6.2.Variable volume fed-batch

     

    In a variable volume fed-batch fermentation, an additional element should be considered: the feed. Consequently, the volume of the medium in the fermenter varies because there is an inflow and no outflow. Again, it is going to be considered that the growth of the microorganism is limited by the concentration of one substrate.

    For the mathematical developments that will be presented, the assumptions are

     

    Table 3.6.2.1. summarizes the equations that apply to this situation. These relations are the base for all further calculations and specific cases of a variable volume fed-batch fermentation.

    Component

      Mass Balance Equation

      Equation #

    Overall F = dV/dt

      (3.6.2.1)

    Biomass dx/dt = x . (u . V -– Kd . V -– F) / V

      (3.6.2.2)

    Substrate ds/dt = F . (so -– s)/V -– u. x/ Yx/s

      (3.6.2.3)

    Product dP/dt = qp . x -–P . F / V

      (3.6.2.4)


    To obtain the derivations that yielded these equations, please click here.
     

    For a non-growth associated product

    In this case it is desirable to have a high cell density. The process can be then divided in two stages: the first stage of the process would therefore be to grow up a high cell concentration, followed by a phase where growth is suppressed and only sufficient of the substrate is supplied for maintenance and product formation the batch feeding phase. The first stage can be translated by the equations in table 3.6.2.1. For the second stage, u should be zero and the production formation rate is defined as rp = beta. x15 .

     

    s = 0;      ds/dt = 0      and      rx= 0                                          &n bsp;                              (3.6.2.5)

    x = K1 . Kd . exp(-Kd . t)/(1 – K1 . K . exp(-Kd . t))                                 &nb sp;           (3.6.2.6)

    Where K1 is defined as the ratio xo / ( Kd + K . x)                                     ;           (3.6.2.7)

    F/V = K . x                                     ;                                          &n bsp;                               (3.6.2.8)

    where K = { ms + b/ Yp/s’} . 1/so                                     &nb sp;                                     (3.6.2.9)

    P= beta / K . [ 1 -– exp (-K . f(t)]                                                                            (3.6.2.10)

     

    A similar and a much simpler development would be implemented if Kd would be negligible. In this situation, the solutions for biomass concentration, flow rate, product concentration and volume variations with time would be given by

    x = xo / (1 + K . xo . t)                                          &nbs p;                                          & nbsp;               (3.6.2.11)

    F = K . xo. Vi                                 &nb sp;                                                                &nb sp;                (3.6.2.12)

    (where Vi is the volume in the beginning of the fed-batch phase)

    P = beta . x . t / (1 + K . x . t)                                    &nb sp;                                                      (3.6.2.13)

    V = Vi . (1 + K . xo.t)                                                                           &nb sp;                           (3.6.2.14)

    Figure 3.6.2.1. depicts the change in volume, product concentration, feed and biomass concentration with time for a fermentation as described above.

    Figure 3.6.2.1. Time profiles for a variable-volume fed-batch culture for a process involving non-growth associated production. V=volume of the fermentor, P=product concentration, u=specific growth rate, X=biomass and S(gls)=growth limiting substrate concentration. The feed follows a similar profile to that one of the specific growth rate.

     

    To obtain the derivations that yielded these equations, please click here.

    For a growth associated product13

    In this case, substrate is provided in such a way that maximizes the specific growth rate, assuming that the substrate is not growth or product formation inhibitory for that concentration. The substrate is supplied here not only for maintenance and product formation but also for biomass production. The product formation is such that rp = alpha . u. x15 , being alpha a specific constant of the bioprocess.

    For a matter of simplicity, Kd is going to be considered to be approximately zero and

    s = constant;      ds/dt = 0                                            ;                                          &n bsp;   (3.6.2.15)

    x = K1 . u. exp(-u . t)/( K1 . K . exp (-u . t) - 1)                                          &nbs p;          (3.6.2.16)

    K = - { u/ Y'x/s’ + ms + alpha . u/ Y'p/s’} . 1/S                                                     (3.6.2.17)

    and K1 is defined as the ratio xo / (u + K . x)                                                            (3.6.2.18)

     

    For product variation with time

    P = alpha . u / K . { 1 -– exp (-K . F(t)}                                      &n bsp;                             (3.6.2.19)

     

     

     

      Figure 3.6.2.2. Time profiles for a variable-volume fed-batch culture for a process involving growth associated production. V=volume of the fermentor, P=product concentration, u=specific growth rate, X=biomass and S(gls)=growth limiting substrate concentration.

     

    To obtain the derivations that yielded these equations, please click here.

    Microorganisms growing exponentially29

    Another approach to a situation in which the specific growth rate is maintained constant goes as following.

     

    F = u . xo . Vo . exp(u . t)/[(so -– s) . Y x/s]                             &n bsp;                                  (3.6.2.20)

    V = Vo (u + A . xo . exp(u . t) – A . xo)/ uwhere

    A = u / (s . Y x/s)                                &nbs p;                                          & nbsp;                            (3.6.2.22)  

    x = u . xo . exp(u . t)/ (u + A . xo . exp(u . t) -– A . xo)                                &nbs p;              (3.6.2.23)

     

    To obtain the derivations that yielded these equations, please click here.

     

    Another alternative would be to maintain the concentration of biomass constant with time – the quasi-steady state6. In this case,

     

    V = Vo + F . t                                 &nb sp;                                                                                (3.6.2.24)

     

    s = F. t/ (Vo + F . t) . (so -– x/ Y x/s)                                      &nbs p;                                       (3.6.2.25)

     

    Which, for small times, approximates zero and for large times approximates

     

    S = so -– x/ Y x/s                                                                           &nb sp;                                                                      (3.6.2.26)

     

    The growth rate varies as following

    For small times: du/dt = -F2/Vo2                             ;                                          &n bsp;                                   (3.6.2.27)

     

    For large times du/dt = -1/t2                                                                           &nb sp;                                        (3.6.2.28)

     

    Which shows that the specific growth rate decreases more in the beginning of the fermentation but decreases less as the time passes by6.

      To obtain the derivations that yielded these equations, please click here.

     

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    3.6.3. Models of possible situations that may occur in a fed-batch fermentation

     

    The models that are presented here can be directly used in the equations summarized in table 3.6.3.1.

     

    Table 3.6.3.1. List of growth models that can be found in biotransformations1

    Model Form
    Monod

      Constant yield

    u = umax s/(K m + s)

    Y x/s = Y0

    Substrate inhibition

      Constant yield

    u = umax s/(Km + s + s2/Ki)

    Y x/s = Y0

    Substrate inhibition

      Variable yield

    u = umax s (1 -– T. s)/(K m + s + s2/Ki)

    Y x/s = Y0 (1 -– T. s)/(1 + R. s + G. s2)

    Substrate and product inhibition

      Inhibitions

      Constants yields

    u = umax s/(Km + s + s2/Ki)

    u = umax o (1 -– P/P m )

    q p = alpha. u+ beta

    alpha, beta and Y p/s

    Ki refers to inhibition constants and have the same units as the substrate concentration (mass of substrate/volume). Tand Rare constants with units that are volume/mass substrate and G has (volume/substrate)2 units. These constants are defined by experimental data analysis1.

     

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    3.7. Parameters used to control fed-batch fermentations

    All the parameters that are about to be described have as an ultimate aim, to control a fed-batch fermentation, more specifically the growth rate and/or the flow through the central carbon metabolism and/or to reduce the overflow of carbon source to metabolic by-products. The control can be a one-step type in which only one of the parameters is used or it can be dual-level control in which two parameters are used, yielding a more "refined" control25, 29, 4. For example, some processes require the control of different parameters at different stages of the fermentation. Such is the example of high density bacterial fermentation like the production of baker's yeast and penicillin. In these cases, as an example, two phases can be distinguished: (i) a phase in which the substrate needs to be controlled so as to avoid by-products formation and (ii) a second stage in which, due to the high cell density, oxygen transfer is limiting and so,this parameter is the one to be controlled above a critical value, under which the cellular metabolism changes. The control constraints switch from specific growth rate to oxygen concentration after some critical period of time in the fermentation process4.

    The choice of each parameter is system dependent and the decision should be based on convenience and experimental data25. The mathematical model is used in two ways: first to estimate the controlling variable and second to calculate the control action4.

    A very important fact that should be considered is the quality of the sensors available for the variables that are whished to be controlled. Temperature, speed of agitation, flow rates, pH, dissolved oxygen, redox potential of broth are examples of commonly controlled variables. These sensors usually respond quickly enough (faster than the change of the variable itself in the system) and so, proportional feedback controllers are often suitable for these variables. Of particular interest, the dead time - time for the sensor to start responding - and the overall time constant - time required to yield the final reading. The crucial design factor is the ratio of the first order time constant to the dead time4. Cohen-Coon derived the following expression to determine the proportionality constant of proportional controllers:

    Kc = Tp/ (Kp . td) . [1 + td / (3Tp)]                                    &nbs p;                                          & nbsp;  3.7.1.

    where

    The steady stater error for this controller can be defined by being equal to -1/(1+KcKp).

    Proportional - integral (PI) and proportional - integral - derivative (PID) controllers14 can also be used, yielding a more refined control and eliminating the set-point offset usually related with proportional controllers. Even when these "more effective" controllers are used, some problems can still occur due to nonlinearities inherent to the process 4.

    To design a feedback controller, a certain parameter to be maintained within certain limits is analyzed as far as requirements to keep its value within the desired range or level. The process response curve, an open loop response of the pH to a step change is generated by changing the value of the parameter by small increments.

    Computer technology allows the handling of mathematical models which are solved on-line and predict and evaluate the future performance.

    Because of some difficulties with measurement of some variables, some linear estimation of state can be used such as the Kalman filter.The Kalman filter uses past measurements for a weighted least square estimate of the current variable as reflected through the dynamic model4. Another alternative is the use of a Dynamic Matrix Control, which is basically a linear dynamic mathematical modelof the process that calculates the response resulting from initial conditions, disturbances, manipulated variable inputs and setpoint changes. The compensation is then applied in such a way that minimizes the sum of squares of deviations from the setpoint,subject to constraints on the manipulated variable4.

    3.7.1. Calorimetry 

    Calorimetry is an an excellent tool for monitoring and controlling microbial fermentations11. Its main advantage is the generality of this parameter, since microbial growth is always accompanied by heat production, and the measurements are performed continuously on-line without introducing any disturbances to the culture. Moreover, the rate of heat production is stoichiometrically related to the rate of substrate consumption and product, including biomass formation. In many cases it can be replaced by exhaust gas analysis, although this approach can not be considered in anaerobic processes which proceed without formation of gaseous products.

    This technique has been proved successful to indirectly determine the substrate and product concentrations continuously during aerobic batch growth of Saccharomyces cerevisiae with glucose as the carbon and energy source. In the presence of this substrate, this yeast shows diauxic growth by initially consuming the glucose with concomitant production of ethanol and then, once glucose is depleted, using the produced ethanol as an energy source. Calorimetry can then be used to control the feed rate in such a way that ethanol formation is avoided.

    Another interesting description of a temperature-based controlled reactor follows a stability criterion that predicts that the range of operation is controlled by the reactant feed, being the flow rate of the cooling medium the control variable23. Although the study has been performed in a chemical reactor, the concepts can be easily extended to a biotransformation process.

    3.7.2. Specific growth rate 

    For the production of a growth-associated product, the production of a certain product is related with the specific growth rate of the producing microorganism. Consequently, it is of interest to feed the fermentor in such a way that the specific growth rate remains constant. Such is the case of the production of hepatitis B surface antigen by Saccharomyces cerevisiae 1, 2. The yield of the antigen is ten times more than that of the fed-batch cultivation for the same volume and total substrate added. Care should be given to the value of the chosen specific growth rate, because cells may not be "activated" easily19, stress proteases can be produced that may degrade the product19 and also there might be a threshold value of specific growth rate above which there is production of by-products29.

           

           

    3.7.3. Substrate (carbon and nitrogen source)

    Substrate is a particularly important parameter to control due to eventual associated growth inhibitions and to increase the effectiveness of the carbon flux, by reducing the amount of by-products formed and the amount of carbon dioxide evolved.

    An example of adaptive feedback control of glucose concentration is found in the fed-batch production of thuringiensin, –an exotoxin that shows efficacious control against flies, beetles, bugs and mites – by Bacillus thuringiensis8. Glucose concentration was estimated by using empirical correlation equations between the consumed glucose and the values of "Oxygen Uptake Rate" (OUR) and "Carbon Dioxide Production Rate" (CPR). Then, the glucose concentration G(t) in the fermentor was expressed as

      G(t) = [{initial mass amount} -– {consumed mass} + {mass in feed}]/V(t)                   (3.7.3.1.)

           

    G(t) = [Gi . Vi - Gcons(t) + Gf . Va]/V(t)                                           &nb sp;                              (3.7.3.2.)

           

    Where

    The equation for adaptive control of substrate addition is

    dG(t)/dt = a . G(t) + b . u(t)                                &nbs p;                                          & nbsp;             (3.7.3.3.)

    Where

    Now, the model strategy is given by

    dG'’(t)/dt = A . [G'’(t) -– Gs]                                         &nb sp;                                                 (3.7.3.4.)

    being A a negative constant, G’(t) the value of glucose concentration that is estimated and Gs the setpoint of G(t). An error signal E(t) can be defined as

     

    E(t) = G(t) -– G'(t)                                  &n bsp;                                           ;                          (3.7.3.5.)

     

    Combining equations 3.7.3.3., 3.7.3.4. and 3.7.3.5., gives

     

    dE(t)/dt = A . E(t) + (a –- A) . G(t) + b . u(t) + A . Gs                                          ;       (3.7.3.6.)

     

    By making the error signal approach zero,

     

    dE(t)/dt = A . E(t)                                  &nb sp;                                                                        (3.7.3.7.)

     

    Then, the feeding rate is determined by combination of equations (3.7.3.6.) and (3.7.3.7.)

     

    u(t) = - 1/b . (a -A) . G(t) - 1/b . A . Gs                              &nb sp;                                         (3.7.3.8.)

     

    By using this adaptive type of control, the production of thuringiensin was significantly improved, with readings that were ten times higher for fed-batch (according to the feed medium) as compared with batch fermentation8.

    A predictive and feedback control algorithm can be also set up to form a product or grow cells such as E. coli 9. The control in this case will be more refined than that of a feedback control. Basically, the control scheme can be divided in two: a feed-forward component that predicts (according to same statistical method and the previous collected data) the "need" of a certain substrate measurable on line, and a feed-back controller which corrects for minor errors in the predicted "need". These errors can occur in exponentially growing microorganisms, in which the predicted value will be greater than the effective value9 . The main advantage to this system is that the investigator does not need to know the metabolic constants for a given organism prior to growth of that organism in the system, and it can be applied to any substrate that can be measured on-line, being particularly valuable in the minimization of by-products.

    In some other situations such as alpha-amylase production in recombinant Bacillus brevis, the fermentation kinetics are mainly driven by the nitrogen source, since this microorganism responds very slowly to glucose depletion and it prefers a nitrogen source over a carbon nutrient for growth and production of recombinant protein16. However, when a large amount of nitrogen source is fed, the larger the cell mass is produced but the lower the recombinant gene production is. Therefore, the feed nitrogenous sources need to be maintained at low levels and can be provided in optimal manner using L-amino acids concentrations control at various levels on-line17.

    As a final comment the operator should be aware of the analytical equipment that will be using so as to guarantee that the readings from the substrate concentrations fall within the limits of detection of the assay and/or analytical assay. At the same time, the operator should make sure that the concentrations are low enough to prevent by-product formation21. Another aspect to consider are eventual interferences in the readings of this due to some other component that might be present in the growth medium.

     

     

    3.7.4. By -product concentration

    The production of by-products is undesirable because reduces the efficacy of the carbon flux in a fermentation. The production of these components take place whenever the substrate is provided in quantities that exceed the oxidative capacity of the cells. This approach has been used in the fermentation of Saccharomyces cerevisiae, in which acid production rate is used to provide on-line estimates of the specific growth rate1. Also, in modern fed-batch processes for yeast production, the feed is under strictly control based on the measurement of traces of ethanol in the exhaust gas of the fermenter22.

     

    3.7.5. Inductive, enhancer or enrichment components

    In certain fermentations it is of interest to continuously add either an inductive or fast consumed components and not only a limiting substrate. An example is the continuous addition of an antibiotic in recombinant microorganims bearing an antibiotic marked plasmid29. Another example is given by the production of gluthathione by high-gluthathione-accumulating Saccharomyces cerevisiae, the commonly microorganims used for commercial production. Cysteine was found to be the only amino acid that enhanced gluthathione formation. However, the growth inhibition occurred and it was related to the concentration of cysteine. This problem was then resolved by an adequate addition of cysteine in exponential fed-batch culture without growth inhibition11.

    Fed-batch proves to be an appropriate mode of fermentation in microorganisms that are producing heterologous proteins and whose elevated protein expression results in product degradation by activation of proteases. A general insight on this subject was the study of a recombinant E. coli for production of chloramphenicol acetyltransferase. A gradual induction with IPTG and phenylalanine (rate limiting precursor) addition strategies were able to reduce the physiological burden imposed on the bacterium, thereby avoiding cellular stress responses and enhancing bioreactor productivity19. In this case, IPTG and phenylalanine were the driving parameters that dominated the feed.

    As a final note, the addition of precursors or inducers should take into account if the product of interest is growth associated or not. For example, the use of a tyrosine-deficient strain of E. coli in the production of phenylalanine requires a balance feed of tyrosine that, if not provided in low quantities is used as carbon source with subsequent production of excessive biomass synthesis at the expense of phenylalanine synthesis. This limitation on biomass production is possible because the phenylalanine production was not growth associated19.

     

     

    3.7.6. Respiratory quotient (RQ)

    Gas analyzers,especially mass spectrophotometers are relatively fast4. Respiratory quotient, the ratio between the moles of carbon evolved per moles of oxygen consumed, has been a general method used to determine indirectly the lack of substrate in the growth medium4. It is a fairly rapid method of measurement that is useful because the gas analyses can be related to crucial process variables. The method is not "universal"to all bioprocesses since some biosystems can produce by-products that affect the productivity of the process without affecting the RQ, such as the production of acetic acid by E.coli4.

    Usually, the signal is characterized by a sharp rise in dissolved oxygen13. The process response of RQ can be represented very closely by a first order transfer function defined by RQ/ (feed of substrate). Equation 3.7.1. can be still used but, any steady state offset for a proportional controller in this case is not desirable. Instead, a PI can be considered.

    Based on the concept of respiratory quotient, there are the so called DO -stats, in which the feed is regulated in accordance with the dissolved oxygen29. The analysis of the dissolved oxygen or carbon dioxide evolution rate can also be used to control or prevent the production of by-products, 1, 10. The respiratory quotient is often analyzed to study the carbon flux, this is, the feed should be conditioned in such a way that it should prevent excess of carbon dioxide evolution caused by unnecessarily severe substrate limitation4,9.

    Care should be given to the mathematical model so that equations are explanatory for certain substrates limits or ranges for which below or above the system behaves differently due to different metabolic reactions and,consequently, different metabolism. Suppose that the desirable point of operation is at RQ=1,corresponding to zero by-product formation (such is the case with Baker's yeast). However, if the substrate feed rate is further reduced, the RQ will remain at 1 but suboptimal conditions will occur. Conversely,RQ can be still equal to 1 if that is the steicheometry of the consumption of the by-product as alternative energy source4. The objective thus is slightly modified to control RQ as near to 1 as possible, but just slightly larger like 1.024. For most processes,amore reliable control system is required4.

     

     

    3.7.7.General feeding mode

    The feeding mode influence a fed-batch fermentation by defining the growth rate of the microorganisms and the effectiveness of the carbon cycle for product formation and minimization of by-product formation. Inherently related with the concept of fed-batch, the feeding mode allows many variances in substrate or other components constitution24 and provision modes and consequently, better control over inhibitory effects of the substrate and/or product. The feed mode can be defined based on an open-loop, if an exact mathematical model is at disposal (not very common and usually insufficient)14, a feedback control (ex. pH - stat or dissolved oxygen (DO) – stat) or in any other way depending on the specific kinetics of each fermentation and even within the time frame of the fermentation process. In fact, the feed can be modified accordingly to the different phases of the microbial growth, as a consequence of physiological alterations that the cells undergo upon transfer through eventual consecutive stages of the fed-batch cultivation10.

    Usually, a fed-batch starts as a batch mode and after a certain biomass concentration or substrate consumption, the fermentor is fed with the limiting susbtrate solution. However, that approach does not need to be the absolute rule. Some cases happen in which the rate of production of a certain product is limited not only by the susbtrate but also by a primary product, associated with the growth of the microorganism. That is the case of streptokinase formation. Streptokinase is a vital and effective drug for the treatment of myocardinal infection, that is currently produced in industry by mainly natural or mutated strains of streptococci. The specific growth rate is inhibited by the susbtrate and by lactic acid. A near optimal feed policy based on a chemotaxis algorithm has been established that defines an initial decreasing feeding phase, followed by a batch fermentation with no more added substrate in the medium. The starting point was the data provided by the batch fermentations and the feed was defined as being a polynomial function of time. By iterative calculations and having the batch time fermentation or the maximum allowable volume of the fermentor as time limits, a feed strategy was defined yielding a 12% increase in streptokinase activity over batch fermentations16. This type of approach has been previously suggested also for ethanol production by Saccharomyces cerevisiae that follows the same kinetics16.

    Finally, the feed can be continuous, can be provided in pulses24, as a shot feeding11, single or multisubstrate24, increasing linearly19, be exponential 7,19 or constant with time. The design of the feed solution may follow a conventional approach – in which the nutrients are more concentrated as compared with the growing medium in the fermentor - or follows a quantitative design in such a way that depletion or accumulation of nutrients can be avoided or reduced28. An optimization problem for a feed to the production of a non-growth associated product is given by Meszaros14.

    3.7.8.Proton production

    An "unusual" type of controlling process parameters is the proton production to estimate on-line the specific growth rate in a fed-batch culture and indirectly, the substrate concentration. In an anaerobic alcohol fermentation, Won et al.27 defined specific growth rate (u) as being

     

    u= dln(proton production)/dt                                   ;                                          &n bsp;    (3.7.8.1.)

     

    The measured amount of proton produced during the fermentation was calculated based on the volume of base added to the fermentor to control the pH at a pre-set value.

    The control based on pH usually uses a on-off mode because the magnitude of the acid and alkali feeds is so low that implemententing a proportional controller is difficult. On -off operation is similar to proportional control with a very high gain because a small amount of acid/alkali feed raises the pH above the set point. Flow must be discontinued to await the reaction to bring the pH back down to the desired value. A variation on the on-off control valve system is frequency modulation. If the pH is very far from the set point, the valve will be open for a long period of time and closed for a shorter period of time. The reversal happen when the pH is in the vicinity of the setpont value. The frequency modulated on-off controller offers more accurate control if that is needed4.

     

    3.7.9. Fluorescence

    A linear relationship exists between the culture fluorescence (as a function of the intracellular NAD(P)H pool) and the dry cell weight concentration up to 30g dry cell weight/liter29. Thus, fluorescence can be used to estimate on-line the biomass concentration and be a controlling parameter in the feed provision29.

     

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    3.8.Parameters to start and finish the feed, and stop the fed-batch fermentation

     

    The times at which the feeding should start and finish, as well as the criteria to stop a fed-batch fermentation is very much dependent on the specific cultivation kinetics and the operator’s interest. For example, in substrate limited processes, the feed should start immediately after all substrate is consumed from the batch phase, otherwise the process may be difficult to control, for example, because of a lag phase due to previous starvation13. The most commonly criteria to start the feed is the depletion of substrate24, which can be measured by a multitude of techniques, from specific enzymatic assays, HPLC25 to indirect methods such as the exhaust gas analysis7, 9. Still related with the amount of substrate in the medium, the operator might not find necessary to reach the complete depletion but to be below a predetermined set-point (eventually related with historical data, growth models and known yields) 8,19.

    The fed-batch fermentation should be halted when the production slows down because of cell death13, because the metabolic potential of the culture becomes inadequately low or because by-product excretion starts at significant levels10. Some other criteria can be an increase in viscosity that implies an increased oxygen demand until the oxygen limitation is achieved, which is the case for penicillin production22.

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    3.9.Preliminary knowledge required to implement fed-batch

     

    Before starting a fed-batch process, a batch fermentation should be implemented to "get to know" the fermentation of the microorganism. From a batch fermentation, the operator should have a knowledge of:

    Now, the operator should define the objective functions and the best parameter to control the fermentation, considering both accuracy of data and convenience. Also, the operator should define if the control that wishes to be implemented is based on an feedback control (direct or indirect) or an open-loop control based on mathematical models established for the system.

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    3.10.Algorithms for operating a fed-batch reactor at optimum specific growth rate (model independent and applicable to adapting systems) 1

         

    The control of a fed-batch fermentation can implicate many difficulties: low accuracy of on-line measurements of substrate concentrations, limited validity of the feed schedule under a variety of conditions and prediction of variations due to strain modification or change in the quality of the nutrient medium. These aspects point to the need of a fed-batch fermentation strategy which is model independent, identifies the optimal state on-line, incorporates a negative feedback control into the nutrient feeding system and contemplates saturation kinetic model, variable yield model, variation in feed substrate concentration and product inhibited fermentation. The following described algorithms describe methods for operating a fed-batch fermentor at the maximum possible rate of fermentation (so that the productivity is maximized). The only requirement is the establishment of a reliable on-line estimate of the specific-fermentation rate1.

         

    3.10.1. Open-loop performance

    In an open-loop operation system, a predetermined feed schedule is used1. This approach considers that the system can be exactly translated in a set of mass balance equations in which the specific growth rate. However, it is easy to assume that due to a non-identified physiological problem of the cells the specific growth rate can be either higher or lower than the one that was previously established. If, for example, the specific growth rate is higher than the pre-set one, and if the substrate is being fed in such a way that is assumed that all the substrate is being consumed as soon as it enters the fermentor, then there will be substrate limitation during the course of the fermentation. Consequently, the open-loop feed policy does not always result in an optimal operation.

         

    3.10.2. Feed-back control algorithm

    This algorithm requires only a reliable on-line estimate of the specific growth rate, that can be provided by any of the parameters described in sections 3.7.1. to 3.7.9. Since the objective of the algorithm is to optimize the cell-mass production by controlling the specific growth rate (u) at an optimum value uopt, the feedback law can be defined:

         

    Fin(t n+1) = Fin (tn) ± Kc [u opt (tn) -u(tn)]                                        &n bsp;                    (3.10.2.1.)

     

    This relation can be used to manipulate the feed flow rate (Fin) to the fermentor, where Kc is a controller constant which is assumed to be positive. When u is different from uopt, either S < Sopt or S > Sopt. Then, the positive sign in equation (3.10.2.1.) applies to the former case and, similarly, the negative sign applies to the latter case. By analysis of what has just been described, then m opt and Sopt need to be identified. Figure 3.10.2.1.describes a flow diagram of the simple control algorithm to find those values by an initial open-loop period. This period continues until m starts to decrease. The maximum value of m obtained during this period is set as uopt and the corresponding value of S as Sopt.

     

    Figure 3.10.2.1. A flow diagram of the control agorithm1.

         

    In situations where it is difficult to obtain on-line measurements or estimates of S, it is proposed to estimate S as S’ and Sopt as Sopt ’ during the open-loop period, in which m opt value is identified. Figure 3.10.2.2 shows the flow diagram that includes all the features that has just been described. This algorithm is model independent and therefore can be applied to many industrial fermentations which utilize complex media. Moreover, since the values of mopt and Sopt are continuously being updated, the control methodology should work well even when the microbial system undergoes adaptation.

     

    Figure 3.10.2.2. A flow diagram of the control algorithm including estimates of optimum substrate and specific growth rate1.

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    3.11. Some examples of fed-batch use in industry

     

    The use of fed-batch culture by the fermentation industry takes advantage of the fact that the concentration of the limiting substrate may be maintained at a very low level, thus

    Saccharomyces cerevisiae is industrially produced using the fed-batch technique so as to maintain the glucose at very low concentrations, maximizing the biomass yield and minimizing the production of ethanol, the chief by-product13, 15, 22.

    Hepatitis B surface antigen (HbsAg) used as a vaccine against type B hepatitis has been purified from human plasma and expressed in recombinant yeast, being now produced commercially. Again, the production of the recombinant protein is achieved using fed-batch culture techniques very similar to that developed for Saccharomyces cerevisiae. A cyclic method is used due to reports of superior productivity22.

    Penicillin production is an example for the use of fed-batch in the production of a secondary metabolite. The fermentation is divided in two phases: the rapid-growth phase during which the culture grows at the maximum specific growth rate, and the slow-growth phase in which penicillin is produced. During the rapid-growth phase, an excess of glucose causes an accumulation of acid and a biomass oxygen demand greater than the aeration capacity of the fermentor, whereas glucose starvation may result in the organic nitrogen in the medium being used as a carbon source, resulting in a high pH and inadequate biomass formation. During the production phase, the feed rates utilized should limit the growth rate and oxygen consumption such that a high rate of penicillin synthesis is achieved and sufficient dissolved oxygen is available in the medium 15, 22.

    Some other examples are the production of thiostrepton from Streptomyces laurentii and the production of cellulase by Trichoderma reesei. The production of thiostrepton uses pH feedback control and the production of cellulase utilizes carbon dioxide production as a control factor15.

     

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